The push, which is designed to grant Congress the role of an “observer” in the high-stakes talks, involves resurrecting the responsibilities of an obscure and little-known congressional body known as the Senate Arms Control Observer Group.

Today, that body operates as the National Security Working Group (NSWG), a bloc of 20 senators co-chaired by Sens. Jim Risch (R-ID) and Dianne Feinstein (D-CA). Lawmakers want to use the NSWG as a vehicle for direct congressional involvement in the nuclear talks between President Donald Trump and the North Korean dictator.

When asked about the NSWG’s efforts, many senators, including members of the foreign relations committee, did not even know that the body existed—neither in its past nor current form.

“I haven’t been keeping up with it,” said Sen. Richard Shelby (R-AL), who recounted a trip to Geneva in the late 1980s with the group shortly after it was formed.

The NSWG’s internal machinations remain largely secretive. Feinstein told The Daily Beast that the group had recently welcomed guest speakers including Defense Secretary James Mattis to discuss a range of issues.

But the group’s official charter notes that senators are authorized to “act as official observers on the United States delegation to any negotiations to which the United States is a party regarding the reduction, limitation, or control” of weapons of mass destruction. And because of that authority, at least one top senator is now making the case that the NSWG would be an ideal conduit for congressional involvement in the North Korea talks.

“The desire is for it to be an observer in any negotiations,” Sen. Bob Menendez (D-N.J.), the top Democrat on the Senate Foreign Relations Committee, told The Daily Beast. “I agreed with Sen. Feinstein and Sen. Risch that I’d be happy because that’s an expanded group that has senior [foreign relations committee] members, senior armed services people, senior intelligence people—so it would be a good group. And we’ll see whether we can get the administration to agree.”

Established in a bipartisan fashion during the height of the Cold War in 1985, the Senate Arms Control Observer Group was envisioned as a way to essentially give Congress a seat at the table on the front end of negotiations with the Soviet Union. The group was created so that lawmakers could exercise more than simply the routine oversight conducted by the foreign relations committee by giving senators a seat at the table during the executive branch’s arms-control negotiations. Its relevance began to fade during the Bill Clinton and George W. Bush administrations as nuclear-related issues were overtaken by other, more pressing foreign-policy matters.

Other lawmakers, however, worry that Congress might throw the White House off if it engages too directly. In particular, some believe that with the negotiations in their nascent stages, the legislative branch should allow traditional committees to have their oversight roles. Already, the Senate Foreign Relations Committee has requested staff-level briefings from the State Department and the National Security Council, aides from both sides of the panel said. And Micah Johnson, a spokeswoman for Sen. Bob Corker (R-TN), the chairman of that committee, said members will “conduct appropriate oversight,” and added that committee hearings and member-level briefings could come eventually. Corker is also in regular contact with Pompeo.

Risch, who is next in line to become chairman of the foreign relations committee and has largely supported Trump in the foreign-policy realm, did not appear to be enthusiastic about the prospect of the NSWG stepping in at such an early stage.

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“Obviously, that is an opportunity we have for oversight,” the senator told The Daily Beast when asked about the NSWG’s efforts. “This whole thing is fluid at this point. The president has been doing really well on this, and we want to see him continue to do that.”

The degree to which Congress does end up demanding a role in any North Korea deal has potentially massive consequences on the success of the deal itself. Just last week, many Republican lawmakers and foreign-policy officials criticized former President Barack Obama for not having involved lawmakers enough in his own nuclear deal with Iran. Specifically, a common complaint was that the Iran deal would have withstood Trump’s successful attempt to nullify it had it been ratified by the Senate.

Ratification, of course, comes only after a deal is reached by the parties involved. Trump and Kim are not yet at that point. In public and in private, senators fret that the negotiations are delicate. They’re also urging caution even as the Kim regime offers to dismantle a nuclear test site and, more recently, released three American prisoners.

“These are developments that are critical to understanding what happens after a successful June 12 meeting. But there’s a lot that can happen between now and then,” Sen. Cory Gardner (R-CO), a member of Republican leadership and a member of the foreign relations panel, said in an interview. “If the president believes that there is no path forward on denuclearization—and by that, I mean complete, verifiable, irreversible decluearization—the meeting shouldn’t even occur.”

Anything beyond routine oversight as negotiations are ongoing is also likely to be met with stiff resistance from the Trump administration. Marc Short, the White House legislative affairs director, told The Daily Beast that Pompeo would remain “in regular contact” with lawmakers about North Korea, but declined to discuss the possibility of an expanded role for the legislative branch.

Presidents have historically balked at congressional involvement in foreign-policy matters. Obama vigorously opposed legislation, crafted in part by Corker, aimed at giving Congress more oversight and input into the Iran nuclear deal after it was negotiated. The resulting bill passed in the Senate with 98 votes.

The Trump administration might have reasons to be concerned about congressional involvement, said a former top aide to John Kerry, who as secretary of state negotiated the terms of the Iran nuclear deal which Trump effectively scrapped last week.

“There would certainly be fear that that the Hill would leak or spoil the environment for sensitive talks,” said Ilan Goldenberg, the director of the Middle East security program at the Center for New American Security. “On the other hand, we’ve seen from the Iran deal that these types of deals require congressional and bipartisan buy-in. And without it they can die. So this could be a good idea to address that problem.”